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Proof step 13 from proof getsetShort-theorem (previous step)

~32768 ≤ j, j ≤ 32767, ub2i(i2b(j)) < 256, 0 ≤ ub2i(i2b(j)) ⊦ ub2i(i2b(j)) + 256 * b2i(i2b(j >> 8)) = j, (j >> 8)∈byte

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 0 ≤ i ∧ 0 ≤ j → i >> j = i / 2 ^ j
Proof step 15:
¬(0 ≤ j ∧ 0 ≤ 8), ~32768 ≤ j, j ≤ 32767, ub2i(i2b(j)) < 256, 0 ≤ ub2i(i2b(j)) ⊦ ub2i(i2b(j)) + 256 * b2i(i2b(j >> 8)) = j, (j >> 8)∈byte
Proof step 38:
0 ≤ j ∧ 0 ≤ 8, ~32768 ≤ j, j ≤ 32767, ub2i(i2b(j)) < 256, 0 ≤ ub2i(i2b(j)) ⊦ ub2i(i2b(j)) + 256 * b2i(i2b(j / 2 ^ 8)) = j, (j / 2 ^ 8)∈byte

Rule argument

spec: intops inst: name: shiftright-pos-div seq: ⊦ 0 ≤ i ∧ 0 ≤ j → i >> j = i / 2 ^ j subst: [j, i] → [8, j] flags: rewrite

Additional information

Used terms: 8, j